Inventory management is concerned with matching supply with demand and a
central problem in Operations Management. The problem is to find the
amount to be produced or purchased in order to maximize the total
expected profit or minimize the total expected cost. Over the past two
decades, several variations of the formula appeared, mostly in trade
journals written by and for inventory managers. A critical assumption in
the inventory literature is that the demands in different periods are
independent and identically distributed. However, in real life, demands
may depend on environmental considerations or the events in the world
such as the weather, the state of economy, etc. Moreover, these events
are represented by stochastic processes - exogenous or controlled.
In Markovian Demand Inventory Models, the authors are concerned with
inventory models where these world events are modeled by Markov
processes. Their research on Markovian demand inventory models was
carried out over a period of ten years beginning in the early nineties.
They demonstrate that the optimality of (s, S)-type policies, or
base-stock policies (i.e., s = S) when there are no fixed ordering costs
with the provision that the policy parameters s and S depend on the
current state of the Markov process representing the environment. Models
allowing backorders when the entire demand cannot be filled from the
available inventory as well as those when the current demand is lost are
considered. As for cost criteria, we treat both the minimization of the
expected total discounted cost and the long-run average cost. The
average-cost criterion is mathematically more difficult than the
discounted cost criteria. Finally, we generalize the usual assumptions
on holding and shortage costs and on demands that are made in the
literature.
